Value (mathematics)

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In mathematics, value commonly refers to the 'output' of a function. In the most basic case, that of unary, single-valued functions, there is one input (the argument) and one output (the value of the function).

Example: If the function

f

is defined by prescribing that

f (x) = 2 x 2 - 3 x + 1

for each real number

x

, then the input 3 will yield the function value 10 (since indeed $2\cdot3^2-3\cdot3+1 = 10$ ).

The function $f$ of the example is real-valued, since each and every possible function value is real. On the other hand, it is not injective, since different inputs may yield the same value; e.g., $f ( - 1.5) = 10$ , too.

In some contexts, for convenience, functions may be considered to have several arguments and/or several values; also cf. the discussion in the article function. However, strictly seen, this is not an extension, since such functions may be considered as having single families and/or sets as input or output.

Value is also used in other senses, e.g., to specify a certain instance of a variable.

Example:

f (x) = 0

for two separate values of

x

, namely, for

x = 0.5

and for

x = 1

Value (mathematics)

See also